Spatially-adaptive penalties for spline fitting

Australian and New Zealand Journal of Statistics

Volumn 42, Issue 2, 2000, Pages 205-223

  Ruppert, David ^a   Carroll, Raymond J ^b  

^a School of Operations Research and Industrial Engineering   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Additive models; Bayesian inference; Confidence intervals; Hierarchical Bayesian model; Regression splines

Indexed keywords

EID: 0034400642     PISSN: 13691473     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-842X.00119     Document Type: Article

References (27)

1. BOX, G.E.P. & TIAO, G.C. (1973). Bayesian Inference in Statistical Analysis. Reading, MA: Addison-Wesley.
2. CARLIN, B.P. & LOUIS, T.A. (1996). Bayes and Empirical Bayes Methods for Data Analysis. London: Chapman & Hall.
3. DEELY, J.J. & LINDLEY, D.V. (1981). Bayes empirical Bayes. J. Amer. Statist. Assoc. 76, 833-841.
4. DENISON, D.G.T., MALLICK, B.K. & SMITH, A.F.M. (1998). Automatic Bayesian curve fitting. J. Roy. Statist. Soc. Ser. B 60, 333-350.
5. DONOHO, D.L. & JOHNSTONE, I.M. (1995). Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90, 1200-1224.
6. EILERS, P.H.C. & MARX, B.D. (1996). Flexible smoothing with B-splines and penalties (with discussion). Statist. Sci. 11, 89-121.
7. EUBANK, R.L. (1988). Spline Smoothing andNonparametric Regression. New York and Basel: Marcel Dekker.
8. FRIEDMAN, J.H. (1991). Multivariate adaptive regression splines (with discussion). Ann. Statist. 19, 1-141.
9. FRIEDMAN, J.H. & SILVERMAN, B.W. (1989). Flexible parsimonious smoothing and additive modeling (with discussion). Technometrics 31, 3-39.
10. HASTIE, T.J. & TIBSHIRANI, R. (1990). Generalized Additive Models. London: Chapman & Hall.
11. HOLST, U., HÖSSJER, O., BJÓRKLUND, C., RAGNARSON, P. & EDNER, H. (1996). Locally weighted least squares kernel regression and statistical evaluation of LIDAR measurements. Environmetrics 7, 401-416.
12. KASS, R.E. & STEFFEY, D. (1989). Approximate Bayesian inference in conditionally independent hierarchical models (parametric empirical Bayes models). J. Amer. Statist. Assoc. 84, 717-726.
13. LAIRD, N.M. & LOUIS, T.A. (1987). Empirical Bayes confidence intervals based on bootstrap samples (with discussion). J. Amer. Statist. Assoc. 82, 739-757.
14. LINDLEY, D.V. & SMITH, A.F.M. (1972). Bayes estimates for the linear model (with discussion). J. Roy. Statist. Soc. Ser. B 34, 1-41.
15. LUO, Z. & WAHBA, G. (1997). Hybrid adaptive splines. J. Amer. Statist. Assoc. 92, 107-116.
16. MARX, B.D. & EILERS, P.H.C. (1998). Direct generalized additive modeling with penalized likelihood. Comput. Statist. Data Anal. 28, 193-209.
17. MORRIS, C.N. (1983). Parametric empirical Bayes inference: theory and applications (with discussion). J. Amer. Statist. Assoc. 78, 47-65.
18. NYCHKA, D. (1988). Bayesian confidence intervals for smoothing splines. J. Amer. Statist. Assoc. 83, 1134-1143.
19. O'SULLIVAN, F. (1986). A statistical perspective on ill-posed inverse problems (with discussion). Statist. Sci. 1, 505-527.
20. O'SULLIVAN, F. (1988). Fast computation of fully automated log-density and log-hazard estimators. SIAM J. Sci. Statist. Comput. 9, 363-379.
21. RUPPERT, D., WAND, M.P., HOLST, U. & HÖSSJER, O. (1997). Local polynomial variance function estimation. Technometrics 39, 262-273.
22. SIGRIST, M. (1994). Air Monitoring by Spectroscopic Techniques. (Chemical Analysis Series, Vol. 127) Wiley.
23. SMITH, M. & KOHN, R. (1996). Nonparametric regression using Bayesian variable selection. J. Econometrics 75, 317-344.
24. STONE, C.J., HANSEN, M., KOOPERBERG, C. & TRUONG, Y.K. (1997). Polynomial splines and their tensor products in extended linear modeling (with discussion). Ann. Statist. 25, 1371-1470.
25. WAHBA, G. (1983). Bayesian 'confidence intervals' for the cross-validated smoothing spline. J. Roy. Statist. Soc. Ser. B 45, 133-150.
26. WAHBA, G. (1990). Spline Models for Observational Data. Philadelphia: Society for Industrial and Applied Mathematics.
27. WAND, M.P. (2000). A comparison of regression splines smoothing procedures. Comput. Statist. (to appear).